The theory of relativity
Einstein stated that the theory of relativity belongs to a class of "principle-theories". As such, it
employs an analytic method, which means that the elements of this theory are not based on
hypothesis but on empirical discovery. By observing natural processes, we understand their general
characteristics, devise mathematical models to describe what we observed, and by analytical means
we deduce the necessary conditions that have to be satisfied. Measurement of separate events must
satisfy these conditions and match the theory's conclusions.[2]
Tests of special relativity
Main article: Tests of special relativity
A diagram of the Michelson–Morley experiment
Relativity is a falsifiable theory: It makes predictions that can be tested by experiment. In the case of
special relativity, these include the principle of relativity, the constancy of the speed of light, and time
dilation.[12] The predictions of special relativity have been confirmed in numerous tests since Einstein
published his paper in 1905, but three experiments conducted between 1881 and 1938 were critical
to its validation. These are the Michelson–Morley experiment, the Kennedy–Thorndike experiment,
and the Ives–Stilwell experiment. Einstein derived the Lorentz transformations from first principles in
1905, but these three experiments allow the transformations to be induced from experimental
evidence.
Maxwell's equations—the foundation of classical electromagnetism—describe light as a wave that
moves with a characteristic velocity. The modern view is that light needs no medium of transmission,
but Maxwell and his contemporaries were convinced that light waves were propagated in a medium,
analogous to sound propagating in air, and ripples propagating on the surface of a pond. This
hypothetical medium was called the luminiferous aether, at rest relative to the "fixed stars" and
through which the Earth moves. Fresnel's partial ether dragging hypothesis ruled out the
measurement of first-order (v/c) effects, and although observations of second-order effects (v2/c2)
were possible in principle, Maxwell thought they were too small to be detected with then-current
technology.[13][14]
The Michelson–Morley experiment was designed to detect second-order effects of the "aether
wind"—the motion of the aether relative to the earth. Michelson designed an instrument called
the Michelson interferometer to accomplish this. The apparatus was sufficiently accurate to detect
the expected effects, but he obtained a null result when the first experiment was conducted in
1881,[15] and again in 1887.[16] Although the failure to detect an aether wind was a disappointment, the
results were accepted by the scientific community.[14] In an attempt to salvage the aether paradigm,
FitzGerald and Lorentz independently created an ad hoc hypothesis in which the length of material
bodies changes according to their motion through the aether.[17] This was the origin of FitzGerald–
Lorentz contraction, and their hypothesis had no theoretical basis. The interpretation of the null result
of the Michelson–Morley experiment is that the round-trip travel time for light
is isotropic (independent of direction), but the result alone is not enough to discount the theory of the
aether or validate the predictions of special relativity.[18][19]
The Kennedy–Thorndike experiment shown with interference fringes.
While the Michelson–Morley experiment showed that the velocity of light is isotropic, it said nothing
about how the magnitude of the velocity changed (if at all) in different inertial frames. The Kennedy–
Thorndike experiment was designed to do that, and was first performed in 1932 by Roy Kennedy
and Edward Thorndike.[20] They obtained a null result, and concluded that "there is no effect ... unless
the velocity of the solar system in space is no more than about half that of the earth in its
orbit".[19][21] That possibility was thought to be too coincidental to provide an acceptable explanation,
so from the null result of their experiment it was concluded that the round-trip time for light is the
same in all inertial reference frames.[18][19]
The Ives–Stilwell experiment was carried out by Herbert Ives and G.R. Stilwell first in 1938[22] and
with better accuracy in 1941.[23] It was designed to test the transverse Doppler effect – the redshift of
light from a moving source in a direction perpendicular to its velocity—which had been predicted by
Einstein in 1905. The strategy was to compare observed Doppler shifts with what was predicted by
classical theory, and look for a Lorentz factor correction. Such a correction was observed, from
which was concluded that the frequency of a moving atomic clock is altered according to special
relativity.[18][19]
Those classic experiments have been repeated many times with increased precision. Other
experiments include, for instance, relativistic energy and momentum increase at high
velocities, experimental testing of time dilation, and modern searches for Lorentz violations.
Tests of general relativity
Main article: Tests of general relativity
General relativity has also been confirmed many times, the classic experiments being the perihelion
precession of Mercury's orbit, the deflection of light by the Sun, and the gravitational redshift of light.
Other tests confirmed the equivalence principle and frame dragging.
Modern applications
Far from being simply of theoretical interest, relativistic effects are important practical engineering
concerns. Satellite-based measurement needs to take into account relativistic effects, as each
satellite is in motion relative to an Earth-bound user and is thus in a different frame of reference
under the theory of relativity. Global positioning systems such as GPS, GLONASS, and Galileo,
must account for all of the relativistic effects, such as the consequences of Earth's gravitational field,
in order to work with precision.[24] This is also the case in the high-precision measurement of
time.[25] Instruments ranging from electron microscopes to particle accelerators would not work if
relativistic considerations were omitted.[26]
Asymptotic symmetries
The spacetime symmetry group for Special Relativity is the Poincaré group, which is a tendimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is
logical to ask what symmetries if any might apply in General Relativity. A tractable case may be to
consider the symmetries of spacetime as seen by observers located far away from all sources of the
gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be
simply to extend and reproduce the symmetries of flat spacetime of special relativity, viz., the
Poincaré group.
In 1962, Hermann Bondi, M. G. van der Burg, A. W. Metzner[27] and Rainer K. Sachs[28] addressed
this asymptotic symmetry problem in order to investigate the flow of energy at infinity due to
propagating gravitational waves. Their first step was to decide on some physically sensible boundary
conditions to place on the gravitational field at light-like infinity to characterize what it means to say a
metric is asymptotically flat, making no a priori assumptions about the nature of the asymptotic
symmetry group — not even the assumption that such a group exists. Then after designing what
they considered to be the most sensible boundary conditions, they investigated the nature of the
resulting asymptotic symmetry transformations that leave invariant the form of the boundary
conditions appropriate for asymptotically flat gravitational fields. What they found was that the
asymptotic symmetry transformations actually do form a group and the structure of this group does
not depend on the particular gravitational field that happens to be present. This means that, as
expected, one can separate the kinematics of spacetime from the dynamics of the gravitational field
at least at spatial infinity. The puzzling surprise in 1962 was their discovery of a rich infinitedimensional group (the so-called BMS group) as the asymptotic symmetry group, instead of the
finite-dimensional Poincaré group, which is a subgroup of the BMS group. Not only are the Lorentz
transformations asymptotic symmetry transformations, there are also additional transformations that
are not Lorentz transformations but are asymptotic symmetry transformations. In fact, they found an
additional infinity of transformation generators known as supertranslations. This implies the
conclusion that General Relativity does not reduce to special relativity in the case of weak fields at
long distances.[29]: